Dittus-Boelter Correlation

Published by F. W. Dittus and L. M. K. Boelter at Berkeley in 1930 (in a university engineering bulletin, not a journal) this is the most-used correlation in heat transfer, and it is deliberately crude. It fits fully developed turbulent flow inside a smooth circular tube, with the stated validity range: Re > 10,000, 0.6 < Pr < 160, and length-to-diameter ratio above about 10 so the entrance region has stopped mattering. Properties are taken at the bulk mean temperature, and the exponent n switches between 0.4 when the fluid is being heated and 0.3 when it is being cooled, which crudely accounts for the way viscosity near the wall changes the velocity profile.

Expect ±25% scatter against experiment, and worse if the wall-to-bulk temperature difference is large or the fluid is very viscous: for those cases Sieder-Tate adds a $(\mu/\mu_{\mathrm{wall}})^{0.14}$ factor, and Gnielinski's 1976 correlation does far better across the transition region. Worked example: Re = 50,000, Pr = 4.5, heating, gives $\mathrm{Nu} = 0.023 \times 50{,}000^{0.8} \times 4.5^{0.4} = 0.023 \times 5743 \times 1.825 = 241$, which in water inside a 25 mm tube is h ≈ 5800 W/(m²·K). The trap worth remembering is the exponent on Re: 0.8 means doubling the velocity buys only 74% more coefficient while the pressure drop rises about fourfold, so there is always a point beyond which pumping the tubes harder is a losing trade.